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President Barack Obama challenged young Africans to shore up progress on the continent that rests on a "fragile foundation," summoning them to fulfil South Africa's beloved former leader Nelson Mandela's vision of equality and opportunity.

Obama, in his own effort to carve out a piece of that legacy, announced a new U.S.-led initiative to double access to electric power across Africa, vowing to help bring "light where there is currently darkness."

The president's remarks at the University of Cape Town capped an emotional day that included a visit to the Robben Island prison where Mandela spent 18 of his 27 years in prison. The 94-year-old anti-apartheid hero has been hospitalized for weeks, with his deteriorating condition serving as both a distraction and an inspiration to Obama throughout his weeklong trip to Africa.

"Nelson Mandela showed us that one man's courage can move the world," Obama said, flanked by a diverse group of young people during his evening speech.

In deeply personal remarks, the U.S. president spoke of standing in Mandela's cramped prison cell Sunday with his two young daughters, Malia and Sasha.

"Seeing them stand within the walls that once surrounded Nelson Mandela, I knew this was an experience they would never forget," he said. "I knew they now appreciated a little bit more that Madiba and other had made for freedom," Obama added, referring to Mandela by his clan name.

Speech evokes famous JFK address

Obama address to a crowd of about 1,100 came nearly 50 years after Robert F. Kennedy delivered his famous "Ripple of Hope" speech at the same university, an address that Obama aides said helped inspire the president's remarks. Kennedy's speech, delivered soon after Mandela was sentenced to prison, called on young people to launch a fight against injustice, creating ripples of hope that would "build a current which can sweep down the mightiest walls of oppression and resistance."

Laying out his own vision for development on the continent where his father was born, Obama said the U.S. seeks "a partnership that empowers Africans to access greater opportunity in their own lives." Harkening back to a prominent theme from his 2009 speech in Ghana — Obama's only other trip to Africa as president — the president said Africans must take much of the responsibility for finishing the work started by Mandela and his contemporaries.

Winnie speaks

Winnie Mandela, 76, said in a U.K. interview published Sunday that her ex-husband has "shown improvement in the past few days." She told The Daily Mail the former president is breathing through an oxygen mask and "there are drips for nutrition and sedation."

"Ultimately I believe Africans should make up their own minds about what serves African interests," he said. "We trust your judgment, the judgment of ordinary people. We believe that when you control your destiny, if you got a handle on your governments then governments will promote freedom and opportunity, because that will serve you."

The White House says Obama's electricity initiative, dubbed "Power Africa," symbolizes the type of cross-continent ventures the president seeks. Backed by $7 billion in U.S. investment, the power program will focus on expanding access to electricity in six African countries: Ethiopia, Ghana, Kenya, Liberia, Nigeria and Tanzania.

"It's the connection that's needed to plug Africa into the grid of the global economy," Obama said of the initiative.

Private companies — including General Electric and Symbion Power — will make an additional $9 billion in commitments aimed at expanding the reach of power grids and developing geothermal, hydro, wind and solar power. However, those contributions fall well short of the $300 billion the International Energy Agency says would be required to achieve universal electricity access in sub-Saharan Africa by 2030.

Despite his focus on building an Africa that can rely on itself, Obama also said the United States would make no apologies for backing efforts to stand up for human dignity on the continent. As long as parts of Africa are ravaged by war, he said, democracy and economic opportunity can't take hold.

Obamas visit Mandela's former jail

He also touted U.S. investment in health programs — particularly an HIV/AIDS program launched by his predecessor, George W. Bush — that have helped millions of Africans access life-saving drugs and reduced the rate of mother-to-child transmission of HIV. The White House said the U.S. will spend $4.2 billion this year on the President's Emergency Plan For AIDS Relief, also known as PEPFAR.

Seeking to highlight the benefits of the initiative, Obama visited a health centre Sunday overseen by Archbishop Desmond Tutu.

The emotional centerpiece of Obama's day was his visit to Robben Island. He was guided on his tour by 83-year-old South African politician Ahmed Kathrada, who was held at the prison for nearly two decades and guided Obama on his 2006 visit to the prison as a U.S. senator.

"On behalf of our family, we're deeply humbled to stand where men of such courage faced down injustice and refused to yield. The world is grateful for the heroes of Robben Island, who remind us that no shackles or cells can match the strength of the human spirit," Obama wrote in the guest book in the prison courtyard, his U.S. Secret Service agents standing watch in the old guard tower above.

Under sunshine and clear, blue skies, Obama, first lady Michelle Obama and daughters Malia and Sasha took in the expansive view of the quarry, a huge crater with views of the rusty guard tower from where Mandela was watched. Obama commented on the "hard labour" Mandela endured and asked Kathrada to remind his daughters how long Mandela was in prison.

Mrs. Obama asked how often Mandela would work and was told he worked daily. As the family turned to leave, Obama asked Kathrada to tell his daughters how the African National Congress, the South African political party, got started.

Obama opened his Africa trip last week in Senegal. He'll travel Monday to Tanzania for the final stop on his tour.